A Simple Test Qualifying the Accuracy of Horner'S Rule for Polynomials, Numerical Algorithms, vol.37, issue.1-4, pp.1-4, 2004. ,
DOI : 10.1023/B:NUMA.0000049487.98618.61
Formal proof for delayed finite field arithmetic using floating point operators, Real Numbers and Computers, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00135090
Formal Verification of Floating-Point Programs, 18th IEEE Symposium on Computer Arithmetic (ARITH '07), 2007. ,
DOI : 10.1109/ARITH.2007.20
URL : https://hal.archives-ouvertes.fr/hal-01174892
Emulation of a FMA and Correctly Rounded Sums: Proved Algorithms Using Rounding to Odd, IEEE Transactions on Computers, vol.57, issue.4, pp.462-471, 2008. ,
DOI : 10.1109/TC.2007.70819
URL : https://hal.archives-ouvertes.fr/inria-00080427
Using reflection to build efficient and certified decision procedures, Proceedings of the Third International Symposium on Theoretical Aspects of Computer Software, pp.515-529, 1997. ,
DOI : 10.1007/BFb0014565
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.7587
The design of the Boost interval arithmetic library, Theoretical Computer Science, vol.351, issue.1, pp.111-118, 2006. ,
DOI : 10.1016/j.tcs.2005.09.062
Generating formally certified bounds on values and round-off errors, Real Numbers and Computers. Dagstuhl, pp.55-70, 2004. ,
URL : https://hal.archives-ouvertes.fr/inria-00070739
Guaranteed Proofs Using Interval Arithmetic, 17th IEEE Symposium on Computer Arithmetic (ARITH'05), pp.188-195, 2005. ,
DOI : 10.1109/ARITH.2005.25
URL : https://hal.archives-ouvertes.fr/hal-00164621
Fast correct rounding of elementary functions in double precision using double-extended arithmetic, Institut National de Recherche en Informatique et en Automatique, 2004. ,
URL : https://hal.archives-ouvertes.fr/inria-00071446
Assisted verification of elementary functions using Gappa, Proceedings of the 2006 ACM symposium on Applied computing , SAC '06, pp.1318-1322, 2006. ,
DOI : 10.1145/1141277.1141584
A comparison of three rounding algorithms for IEEE floatingpoint multiplication, Proceedings of the 14th Symposium on Computer Arithmetic, pp.225-232, 1999. ,
Why: a multi-language multi-prover verification tool, Research Report, vol.1366, 2003. ,
MPFR, ACM Transactions on Mathematical Software, vol.33, issue.2, 2005. ,
DOI : 10.1145/1236463.1236468
URL : https://hal.archives-ouvertes.fr/inria-00070266
Formally verifying an algorithm based on interval arithmetic for checking transversality, Fifth International Workshop on the ACL2 Theorem Prover and Its Applications, p.17, 2004. ,
Floating point verification in HOL light: The exponential function, 1997. ,
DOI : 10.1007/BFb0000475
The HOL Light manual, 2000. ,
Accuracy and stability of numerical algorithms, SIAM, 2002. ,
DOI : 10.1137/1.9780898718027
The Coq proof assistant: a tutorial: version 8, 2004. ,
Applied interval analysis, 2001. ,
DOI : 10.1007/978-1-4471-0249-6
URL : https://hal.archives-ouvertes.fr/hal-00845131
Pracniques: further remarks on reducing truncation errors, Communications of the ACM, vol.8, issue.1, p.40, 1965. ,
DOI : 10.1145/363707.363723
Computer-Aided Reasoning: An Approach, 2000. ,
Formally certified floating-point filters for homogeneous geometric predicates, Theoretical Informatics and Applications 41, pp.57-70, 2007. ,
DOI : 10.1051/ita:2007005
URL : https://hal.archives-ouvertes.fr/inria-00071232
Optimisation d'opérateurs arithmétiques matérielsmatériels`matérielsà base d'approximations polynomiales, Symposium en Architecture de Machines, pp.1318-1322, 2006. ,
Real number calculations and theorem proving, 18th International Conference on Theorem Proving in Higher Order Logics, pp.239-254, 2005. ,
Interval methods for systems of equations, 1990. ,
DOI : 10.1017/CBO9780511526473
PVS: A prototype verification system, 11th International Conference on Automated Deduction, pp.748-752, 1992. ,
DOI : 10.1007/3-540-55602-8_217
Static Analysis-Based Validation of Floating-Point Computations, Novel Approaches to Verification, pp.306-313, 2004. ,
DOI : 10.1007/978-3-540-24738-8_18
Analyse et implantation d'algorithmes rapides pour l'´ evaluation polynomiale sur les nombres flottants, 2006. ,
URL : https://hal.archives-ouvertes.fr/ensl-00119498
Rockwell Collins receives MILS certification from NSA on microprocessor, 2005. ,
Accurate floating-point summation, 2005. ,
Schlumberger leads the way in smart card security with common criteria EAL7 security methodology, 2003. ,
An American national standard: IEEE standard for binary floating point arithmetic, ACM SIGPLAN Notices, vol.22, issue.2, pp.9-25, 1987. ,
Table-driven implementation of the exponential function in IEEE floating-point arithmetic, ACM Transactions on Mathematical Software, vol.15, issue.2, pp.144-157, 1989. ,
DOI : 10.1145/63522.214389
Invisible formal methods for embedded control systems, Proceedings of the IEEE, vol.91, issue.1, pp.29-39, 2003. ,
DOI : 10.1109/JPROC.2002.805818